(u,v) grid of a face extends beyond its edges

I have a face (Geom_BSplineSurface) and I want to draw points or lines in a sort of grid pattern inside that face.

I tried getting the bounds of the face and simply iterating through that (from min to max); I also tried creating iso lines (with ​ShapeAnalysis_Surface::UIso and VIso). In both cases, the grid goes beyond the limits of the face (see attached screenshot).

It seems like the face is trimmed somehow, but I can't figure out how to get information on that trim to get the proper u,v parameters to stay inbounds.

Also, if I have other types of faces, like Geom_CylindricalSurface, I simply cannot get the UV bounds, and I also want to get a grid of points in them. I would like a method to do that without having to treat each type of surface differently.

Any ideas?

Thank you,

Note: In the screenshot, the purple area is the triangulation of the face, and the yellow and cyan lines are ISO curves created with something like this:

ShapeAnalysis_Surface sas(surface);
 
double u1,u2,v1,v2;
sas.Bounds(u1,u2,v1,v2);
 
for (int i = 0; i <= 12; i++)
{
    Handle(Geom_Curve) curveU = sas.UIso(u1 + (u2-u1)*((double)i/12));

//...

//same thing with sas.VIso, using v1 and v2